Finite Group Databasebeta

← Q8×#41×D67 #31762899

Subgroups — Q8×#41×D67 #31762899

Order 17152.

7522 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#11761629C211yesmaximal, characteristic, complemented
2#22573791C213yesmaximal, complemented
3Q8×#11761628C213yesmaximal, complemented
4#41×Dic134C213yesmaximal, complemented
5#22573788C219yesmaximal, complemented
6#22573787C219yesmaximal, complemented
7Q8×#11761627C213yesmaximal, complemented
8Q82×D67C211yesmaximal, characteristic, complemented
9#557×D67C213yesmaximal, complemented
10#554×D67C219yesmaximal, complemented
11D4×Q8×D67C213yesmaximal, complemented
12#533×D67C219yesmaximal, complemented
13C4×#41×D67C213yesmaximal
14C2×C4×Q8×D67C213yesmaximal, complemented
15Q8×#41×C67C211yesmaximal, characteristic, complemented
16C2×#41×D67C2211yescharacteristic
17C22×Q8×D67C2213yes—
18Q8×Dic134C2213yescomplemented
19Q8×Dic134C2213yescomplemented
20#16864126C2219yescomplemented
21#16864125C2213yescomplemented
22#16864124C2219yescomplemented
23#16864123C22118yescomplemented
24#16864122C2216yescomplemented
25#16864121C2219yescomplemented
26#16864107C2219yescomplemented
27#16864106C2219yescomplemented
28#16864105C22118yescomplemented
29#16864104C22118yescomplemented
30#16864103C2219yescomplemented
31#16864102C22118yescomplemented
32#16864101C22118yescomplemented
33#16864100C22136yescomplemented
34Q8×D268C2213yescomplemented
35D4×Dic134C2219yescomplemented
36#16864061C2219yescomplemented
37Q8×C22⋊D67C2216yescomplemented
38#16864059C22118yescomplemented
39#16863953C2219yescomplemented
40#16863952C22118yescomplemented
41#16863951C2219yescomplemented
42#16863951C2219yescomplemented
43#16863950C22118yescomplemented
44#16863950C22118yescomplemented
45#16863949C22118yescomplemented
46#16863948C22118yescomplemented
47#16863948C22118yescomplemented
48C4⋊Q8×D67C2219yes—
49C4⋊Q8×D67C2219yes—
50#125×D67C22118yes—
51C22⋊Q8×D67C22118yes—
52C22⋊Q8×D67C22118yes—
53#41×Dic67C2213yes—
54C4×#11761629C2213yes—
55C4×#11761629C2213yes—
56C4×#11761628C2219yes—
57#16863864C2219yes—
58C4×#11761627C2219yes—
59C4×#11761627C2219yes—
60C2×Q8×Dic67C2213yescomplemented
61C2×C4×Dic134C2219yescomplemented
62C2×#14524008C2219yescomplemented
63C4×Q8×D67C2211yescharacteristic
64C4×Q8×D67C2213yes—
65C4×Q8×D67C2219yes—
66C4×Q8×D67C2219yes—
67C4×Q8×D67C2213yes—
68C4×Q8×D67C2213yes—
69C4×Q8×D67C2216yes—
70C4×Q8×D67C2213yescomplemented
71C4×Q8×D67C2219yescomplemented
72C4×Q8×D67C2219yescomplemented
73C4×Q8×D67C2213yescomplemented
74C4×D4×D67C2219yes—
75C4×D4×D67C2219yes—
76#117×D67C2219yes—
77C2×C4⋊C4×D67C2219yes—
78C2×C42×D67C2219yes—
79Q82×C67C2211yescharacteristic, complemented
80#557×C67C2213yescomplemented
81#554×C67C2219yescomplemented
82D4×Q8×C67C2213yescomplemented
83#533×C67C2219yescomplemented
84C4×#41×C67C2213yes—
85C2×C4×Q8×C67C2213yescomplemented
86C2×#11761629C2311yescharacteristic
87C2×#11761628C2313yes—
88C2×#11761627C2313yes—
89#41×D67Q8116yesdirect product factor
90C22×Dic134C2319yes—
91C2×Q8×D67—224no—
92C2×Q8×D67C2319yes—
93C2×Q8×D67C2313yes—
94C2×Q8×D67C2319yes—
95C2×Q8×D67C2316yes—
96C2×Q8×D67C2311yescharacteristic
97C2×Q8×D67C2311yescharacteristic
98C2×D4×D67C2313yes—
99C22×C4×D67C2319yes—
100C22×C4×D67C2319yes—
101C22×C4×D67C2313yes—
102#14524043C2319yes—
103#14524043C2319yes—
104#14524042C23118yes—
105#14524042C23118yes—
106#14524042C23118yes—
107#14524042C23118yes—
108#14524041C23118yes—
109#14524041C23118yes—
110#14524035C23118yes—
111#14524034C23118yes—
112#14524034C23118yes—
113#14524033C23136yes—
114#14524033C23136yes—
115#14524023C23118yes—
116#14524023C23118yes—
117#14524022C23118yes—
118#14524022C23118yes—
119#14524021C23136yes—
120#14524021C23136yes—
121#14524020C23136yes—
122#14524020C23136yes—
123#14524019C23118yes—
124#14524019C23118yes—
125Q8×Dic67C2313yes—
126Q8×Dic67C2319yes—
127Q8×Dic67C2311yescharacteristic
128Q8×Dic67C2319yes—
129Q8×Dic67C2313yes—
130Q8×Dic67C2313yes—
131Q8×Dic67C2316yes—
132C4×Dic134C2319yes—
133C4×Dic134C23118yes—
134C4×Dic134C2319yes—
135C4×Dic134C2313yes—
136C4×Dic134C23118yes—
137C4×Dic134C2319yes—
138C4×Dic134C2319yes—
139C4×Dic134C2319yes—
140C4×Dic134C23118yes—
141#14524008C2319yes—
142#14524008C23118yes—
143#14524008C2319yes—
144#14524008C2313yes—
145#14524008C2319yes—
146#14524008C23118yes—
147#14524008C2319yes—
148#14524008C2319yes—
149#14524008C23118yes—
150C4×D268C2319yes—
151C4×D268C2319yes—
152D4×Dic67C2319yes—
153D4×Dic67C2319yes—
154#14524005C2319yes—
155#14524005C2319yes—
156C4×C22⋊D67C23118yes—
157C4×C22⋊D67C23118yes—
158(C22⋊D67)⋊C4C23118yes—
159(C22⋊D67)⋊C4C23118yes—
160#14524002C2319yes—
161#14524001C2319yes—
162#14524001C2319yes—
163#14524000C23118yes—
164#14523999C23118yes—
165C2×C4⋊Dic67C2319yes—
166C2×Dic67⋊C4C23118yes—
167C4⋊C4×D67C23118yes—
168C4⋊C4×D67C2313yes—
169C4⋊C4×D67C2319yes—
170C4⋊C4×D67C2319yes—
171C4⋊C4×D67C23118yes—
172C4⋊C4×D67C2319yes—
173C4⋊C4×D67C2319yes—
174C4⋊C4×D67C2319yes—
175C4⋊C4×D67C23118yes—
176C22⋊C4×D67C23118yes—
177C2×C4×Dic67C2319yes—
178C2×C4×Dic67C2319yes—
179C2×C4×Dic67C2319yes—
180C42×D67C2313yes—
181C42×D67C2319yes—
182C42×D67C2319yes—
183C42×D67C2319yes—
184C42×D67C2319yes—
185C42×D67C2319yes—
186C42×D67C2319yes—
187C42×D67C2319yes—
188C2×#41×C67C2311yescharacteristic
189C22×Q8×C67C2313yes—
190C4⋊Q8×C67C2319yes—
191C4⋊Q8×C67C2319yes—
192#125×C67C23118yes—
193C22⋊Q8×C67C23118yes—
194C22⋊Q8×C67C23118yes—
195C4×Q8×C67C2313yes—
196C4×Q8×C67C2311yescharacteristic
197C4×Q8×C67C2319yes—
198C4×Q8×C67C2319yes—
199C4×Q8×C67C2313yes—
200C4×Q8×C67C2313yes—
201C4×Q8×C67C2316yes—
202C4×D4×C67C2319yes—
203C4×D4×C67C2319yes—
204#117×C67C2319yes—
205C2×C4⋊C4×C67C2319yes—
206C2×C42×C67C2319yes—
207C23×D67C2413yes—
208#11761629C2×Q818yescomplemented
209#11761628C2×Q8124yescomplemented
210#11761627C2×Q8124yescomplemented
211C2×Dic134—236no—
212C2×Dic134C24118yes—
213C2×Dic134C2419yes—
214C2×Dic134C24118yes—
215C2×Dic134C2413yes—
216C2×Dic134C2413yes—
217Q8×D67—212no—
218Q8×D67—236no—
219Q8×D67—236no—
220Q8×D67—412no—
221Q8×D67C2×Q818yescomplemented
222Q8×D67#4118yesdirect product factor
223C2×D268C2413yes—
224C2×C22⋊D67C2416yes—
225D4×D67C2×Q8124yescomplemented
226C22×Dic67C2419yes—
227C22×Dic67C2419yes—
228C22×Dic67C2413yes—
229C2×C4×D67—236no—
230C2×C4×D67—418no—
231C2×C4×D67C2×Q8124yescomplemented
232C2×C4×D67C2413yes—
233C2×C4×D67C2419yes—
234C2×C4×D67C2419yes—
235C2×C4×D67C2419yes—
236C2×C4×D67C2419yes—
237C2×C4×D67C2419yes—
238C2×C4×D67C2419yes—
239C2×C4×D67C2411yescharacteristic
240C2×C4×D67C2413yes—
241C2×C4×D67C2413yes—
242C2×C4×D67C2413yes—
243C2×C4×D67C2413yes—
244C4⋊Dic67C2413yes—
245C4⋊Dic67C2419yes—
246C4⋊Dic67C24118yes—
247C4⋊Dic67C2419yes—
248C4⋊Dic67C2419yes—
249C4⋊Dic67C24118yes—
250Dic67⋊C4C2416yes—
251Dic67⋊C4C24118yes—
252Dic67⋊C4C24118yes—
253Dic67⋊C4C24118yes—
254Dic67⋊C4C24118yes—
255Dic67⋊C4C24118yes—
256Dic67⋊C4C24136yes—
257C22⋊Dic67C24118yes—
258(C2×D67)⋊C4C24118yes—
259(C2×D67)⋊C4C24118yes—
260C4×Dic67C2413yes—
261C4×Dic67C2413yes—
262C4×Dic67C2413yes—
263C4×Dic67C2419yes—
264C4×Dic67C2419yes—
265C4×Dic67C2419yes—
266C4×Dic67C2419yes—
267C4×Dic67C2419yes—
268C4×Dic67C2419yes—
269C4×Dic67C2419yes—
270C4×Dic67C2419yes—
271C4×Dic67C2419yes—
272#41×C67C2×Q818yescomplemented
273C2×Q8×C67—212no—
274C2×Q8×C67C2419yes—
275C2×Q8×C67C2416yes—
276C2×Q8×C67C2411yescharacteristic
277C2×Q8×C67C2411yescharacteristic
278C2×D4×C67C2413yes—
279C22×C4×C67C2419yes—
280C22×C4×C67C2419yes—
281C22×C4×C67C2413yes—
282C4⋊C4×C67C2413yes—
283C4⋊C4×C67C24118yes—
284C4⋊C4×C67C2419yes—
285C4⋊C4×C67C2419yes—
286C4⋊C4×C67C2419yes—
287C4⋊C4×C67C24118yes—
288C22⋊C4×C67C24118yes—
289C42×C67C2413yes—
290C42×C67C2419yes—
291C42×C67C2419yes—
292C42×C67C2419yes—
293C23×C67C2513yes—
294C22×D67—26no—
295C22×D67—26no—
296C22×D67C22×Q8112yes—
297C22×D67C2513yes—
298C22×D67C2511yescharacteristic
299Q8×C67—218no—
300Q8×C67—46no—
301Q8×C67C22×Q814yescomplemented
302Q8×C67C2×#4114yescomplemented
303D4×C67C22×Q8112yescomplemented
304C2×C4×C67—218no—
305C2×C4×C67—49no—
306C2×C4×C67C22×Q8112yescomplemented
307C2×C4×C67C2513yes—
308C2×C4×C67C2519yes—
309C2×C4×C67C2519yes—
310C2×C4×C67C2513yes—
311C2×C4×C67C2513yes—
312C2×C4×C67C2511yescharacteristic
313C22⋊D67C22×Q8124yescomplemented
314C2×Dic67—218no—
315C2×Dic67—49no—
316C2×Dic67C22×Q8112yescomplemented
317C2×Dic67C2513yes—
318C2×Dic67C2519yes—
319C2×Dic67C2519yes—
320C2×Dic67C2511yescharacteristic
321C2×Dic67C2513yes—
322C2×Dic67C2513yes—
323D268C22×Q8112yescomplemented
324C4×D67—218no—
325C4×D67—26no—
326C4×D67—218no—
327C4×D67—218no—
328C4×D67—218no—
329C4×D67—49no—
330C4×D67—49no—
331C4×D67C22×Q814yes—
332C4×D67C22×Q8112yes—
333C4×D67C22×Q8112yescomplemented
334C4×D67C22×Q8112yescomplemented
335C4×D67C2×#41112yes—
336Dic134—218no—
337Dic134—236no—
338Dic134—418no—
339Dic134C22×Q8112yescomplemented
340Dic134C2×#41112yescomplemented
341C22×C67—23no—
342C22×C67—23no—
343C22×C67C23×Q816yes—
344C22×C67C2611yescharacteristic
345C2×D67—23no—
346C2×D67—23no—
347C2×D67—224no—
348C2×D67C23×Q816yes—
349C2×D67C23×Q812yes—
350C2×D67C22×#4112yes—
351C2×D67#58512yes—
352C4×C67—29no—
353C4×C67—29no—
354C4×C67—23no—
355C4×C67C23×Q816yes—
356C4×C67C23×Q812yes—
357C4×C67C22×#4116yes—
358Dic67—29no—
359Dic67—29no—
360Dic67—23no—
361Dic67C23×Q816yes—
362Dic67C23×Q812yes—
363Dic67C22×#4116yes—
364C2×Q8×#41—671nomaximal, Sylow
365C2×C67—26no—
366C2×C67C24×Q811yescharacteristic
367C2×C67C23×#4111yescharacteristic
368C2×C67C2×#58511yescharacteristic
369D67—26no—
370D67Q8×#4114yesdirect product factor
371Q8×#41—671no—
372Q8×#41—673no—
373Q8×#41—679no—
374Q8×#41—673no—
375Q8×#41—679no—
376Q8×#41—673no—
377Q8×#41—673no—
378Q8×#41D6711yescharacteristic, direct product factor
379C2×Q82—671no—
380C2×#557—673no—
381C2×#554—679no—
382C2×D4×Q8—673no—
383C2×#533—679no—
384C2×C4×#41—673no—
385C22×C4×Q8—673no—
386C67C2×Q8×#4111yescharacteristic, complemented, Sylow
387C22×#41—671no—
388C23×Q8—673no—
389Q82—679no—
390Q82—673no—
391Q82—673no—
392Q82C2×D6711yescharacteristic, complemented
393#557—679no—
394#557—6718no—
395#557—676no—
396#557—679no—
397#557—673no—
398#557C2×D6713yescomplemented
399#554—679no—
400#554—6718no—
401#554—6736no—
402#554—6718no—
403#554—679no—
404#554—679no—
405#554—6718no—
406#554—6718no—
407#554C2×D6719yescomplemented
408D4×Q8—676no—
409D4×Q8—679no—
410D4×Q8—6718no—
411D4×Q8—673no—
412D4×Q8—679no—
413D4×Q8C2×D6713yescomplemented
414#533—679no—
415#533—679no—
416#533—6718no—
417#533—6718no—
418#533—6718no—
419#533—6718no—
420#533—6718no—
421#533—6718no—
422#533—679no—
423#533C2×D6719yescomplemented
424C2×C4⋊Q8—679no—
425C2×C4⋊Q8—679no—
426C2×#125—6718no—
427C2×C22⋊Q8—6718no—
428C2×C22⋊Q8—6718no—
429C4×#41—673no—
430C4×#41—673no—
431C4×#41—673no—
432C4×#41—679no—
433C4×#41—679no—
434C4×#41—679no—
435C4×#41—679no—
436C4×#41C2×D6713yes—
437C2×C4×Q8—673no—
438C2×C4×Q8—671no—
439C2×C4×Q8—679no—
440C2×C4×Q8—673no—
441C2×C4×Q8—679no—
442C2×C4×Q8—673no—
443C2×C4×Q8—679no—
444C2×C4×Q8—673no—
445C2×C4×Q8—679no—
446C2×C4×Q8—673no—
447C2×C4×Q8—673no—
448C2×C4×Q8—676no—
449C2×C4×Q8—679no—
450C2×C4×Q8—679no—
451C2×C4×Q8C2×D6713yescomplemented
452C2×C4×D4—679no—
453C2×C4×D4—679no—
454C2×#117—679no—
455C22×C4⋊C4—679no—
456C22×C42—679no—
457C2×#41—6716no—
458C2×#41—671no—
459C2×#41—673no—
460C2×#41—673no—
461C2×#41C22×D6711yescharacteristic
462C22×Q8—676no—
463C22×Q8—671no—
464C22×Q8—671no—
465C22×Q8—679no—
466C22×Q8—679no—
467C22×Q8—673no—
468C22×Q8—679no—
469C22×Q8—13424no—
470C22×Q8C22×D6713yes—
471C22×D4—673no—
472C23×C4—679no—
473C23×C4—673no—
474C23×C4—679no—
475C4⋊Q8—6718no—
476C4⋊Q8—6718no—
477C4⋊Q8—6718no—
478C4⋊Q8—6718no—
479C4⋊Q8—6718no—
480C4⋊Q8—6718no—
481C4⋊Q8—679no—
482C4⋊Q8—679no—
483C4⋊Q8C22×D6719yes—
484C4⋊Q8C22×D6719yes—
485#125—6736no—
486#125—6736no—
487#125—6718no—
488#125—6718no—
489#125—6718no—
490#125C22×D67118yes—
491C22⋊Q8—6718no—
492C22⋊Q8—6718no—
493C22⋊Q8—6718no—
494C22⋊Q8—6718no—
495C22⋊Q8—6736no—
496C22⋊Q8—6718no—
497C22⋊Q8—6736no—
498C22⋊Q8—6718no—
499C22⋊Q8—6736no—
500C22⋊Q8—6736no—
501C22⋊Q8C22×D67118yes—
502C22⋊Q8C22×D67118yes—
503C4×Q8—671no—
504C4×Q8—679no—
505C4×Q8—673no—
506C4×Q8—679no—
507C4×Q8—673no—
508C4×Q8—673no—
509C4×Q8—676no—
510C4×Q8—673no—
511C4×Q8—679no—
512C4×Q8—6718no—
513C4×Q8—679no—
514C4×Q8—6718no—
515C4×Q8—679no—
516C4×Q8—679no—
517C4×Q8—679no—
518C4×Q8—6718no—
519C4×Q8—673no—
520C4×Q8—6718no—
521C4×Q8—679no—
522C4×Q8—679no—
523C4×Q8—679no—
524C4×Q8—6718no—
525C4×Q8—679no—
526C4×Q8—679no—
527C4×Q8—6718no—
528C4×Q8C22×D6711yescharacteristic
529C4×Q8C22×D6719yes—
530C4×Q8C22×D6713yes—
531C4×Q8C22×D6719yes—
532C4×Q8C22×D6713yes—
533C4×Q8C22×D6713yes—
534C4×Q8C22×D6716yes—
535C4×D4—679no—
536C4×D4—679no—
537C4×D4—6718no—
538C4×D4—6718no—
539C4×D4—679no—
540C4×D4—679no—
541C4×D4—6718no—
542C4×D4—6718no—
543C4×D4—679no—
544C4×D4—679no—
545C4×D4C22×D6719yes—
546C4×D4C22×D6719yes—
547#117—679no—
548#117—679no—
549#117—679no—
550#117—6718no—
551#117—6718no—
552#117C22×D6719yes—
553C2×C4⋊C4—6718no—
554C2×C4⋊C4—679no—
555C2×C4⋊C4—673no—
556C2×C4⋊C4—6718no—
557C2×C4⋊C4—679no—
558C2×C4⋊C4—6718no—
559C2×C4⋊C4—679no—
560C2×C4⋊C4—679no—
561C2×C4⋊C4—679no—
562C2×C4⋊C4—679no—
563C2×C4⋊C4—6718no—
564C2×C4⋊C4C22×D6719yes—
565C2×C22⋊C4—6718no—
566C2×C42—679no—
567C2×C42—679no—
568C2×C42—679no—
569C2×C42—679no—
570C2×C42—679no—
571C2×C42—679no—
572C2×C42—673no—
573C2×C42—679no—
574C2×C42—679no—
575C2×C42—679no—
576C2×C42—679no—
577C2×C42C22×D6719yes—
578C24—673no—
579#41—678no—
580#41—6724no—
581#41—6724no—
582#41Q8×D6718yesdirect product factor
583C2×Q8—212no—
584C2×Q8—26812no—
585C2×Q8—678no—
586C2×Q8—678no—
587C2×Q8—6718no—
588C2×Q8—673no—
589C2×Q8—673no—
590C2×Q8—6718no—
591C2×Q8—679no—
592C2×Q8—13436no—
593C2×Q8—13436no—
594C2×Q8—13436no—
595C2×Q8—13412no—
596C2×Q8C23×D6719yes—
597C2×Q8C23×D6716yes—
598C2×Q8C23×D6711yescharacteristic
599C2×Q8C23×D6711yescharacteristic
600C2×D4—676no—
601C2×D4—6724no—
602C2×D4—673no—
603C2×D4C23×D6713yes—
604C22×C4—26818no—
605C22×C4—679no—
606C22×C4—679no—
607C22×C4—679no—
608C22×C4—673no—
609C22×C4—6724no—
610C22×C4—673no—
611C22×C4—673no—
612C22×C4—673no—
613C22×C4—671no—
614C22×C4—673no—
615C22×C4—679no—
616C22×C4—673no—
617C22×C4—679no—
618C22×C4—679no—
619C22×C4—679no—
620C22×C4—679no—
621C22×C4—13436no—
622C22×C4C23×D6719yes—
623C22×C4C23×D6719yes—
624C22×C4C23×D6713yes—
625C4⋊C4—676no—
626C4⋊C4—673no—
627C4⋊C4—6718no—
628C4⋊C4—6718no—
629C4⋊C4—6718no—
630C4⋊C4—6718no—
631C4⋊C4—679no—
632C4⋊C4—6718no—
633C4⋊C4—6718no—
634C4⋊C4—679no—
635C4⋊C4—679no—
636C4⋊C4—6736no—
637C4⋊C4—6718no—
638C4⋊C4C23×D6713yes—
639C4⋊C4C23×D67118yes—
640C4⋊C4C23×D6719yes—
641C4⋊C4C23×D6719yes—
642C4⋊C4C23×D6719yes—
643C4⋊C4C23×D67118yes—
644C22⋊C4—6718no—
645C22⋊C4—6718no—
646C22⋊C4—6718no—
647C22⋊C4C23×D67118yes—
648C42—673no—
649C42—673no—
650C42—679no—
651C42—679no—
652C42—679no—
653C42—679no—
654C42—679no—
655C42—679no—
656C42—679no—
657C42—679no—
658C42—673no—
659C42—679no—
660C42C23×D6719yes—
661C42C23×D6719yes—
662C42C23×D6713yes—
663C42C23×D6719yes—
664C23—671no—
665C23—6712no—
666C23—673no—
667C23—1346no—
668C23—1346no—
669C23C24×D6713yes—
670Q8—218no—
671Q8—46no—
672Q8—26818no—
673Q8—6712no—
674Q8—6712no—
675Q8—13436no—
676Q8—13418no—
677Q8C2×Q8×D6714yescomplemented
678Q8#41×D6714yesdirect product factor
679D4—6724no—
680D4—6712no—
681D4C2×Q8×D67112yescomplemented
682C2×C4—218no—
683C2×C4—49no—
684C2×C4—2689no—
685C2×C4—2689no—
686C2×C4—2689no—
687C2×C4—6712no—
688C2×C4—671no—
689C2×C4—673no—
690C2×C4—673no—
691C2×C4—674no—
692C2×C4—6712no—
693C2×C4—6712no—
694C2×C4—6712no—
695C2×C4—6712no—
696C2×C4—673no—
697C2×C4—679no—
698C2×C4—679no—
699C2×C4—13418no—
700C2×C4—1346no—
701C2×C4—13418no—
702C2×C4—13418no—
703C2×C4—13418no—
704C2×C4—13418no—
705C2×C4C2×Q8×D67112yescomplemented
706C2×C4C24×D6713yes—
707C2×C4C24×D6719yes—
708C2×C4C24×D6719yes—
709C2×C4C24×D6713yes—
710C2×C4C24×D6713yes—
711C2×C4C24×D6711yescharacteristic
712C22—23no—
713C22—23no—
714C22—672no—
715C22—672no—
716C22—672no—
717C22—676no—
718C22—13424no—
719C22—1343no—
720C22—1343no—
721C22C22×Q8×D6716yes—
722C22C25×D6711yescharacteristic
723C4—29no—
724C4—23no—
725C4—29no—
726C4—672no—
727C4—676no—
728C4—676no—
729C4—1349no—
730C4—1343no—
731C4—1349no—
732C4C22×Q8×D6712yes—
733C4C22×Q8×D6716yes—
734C4C2×#41×D6716yes—
735C2—26no—
736C2—674no—
737C2—1346no—
738C2C23×Q8×D6711yescharacteristic
739C2C22×#41×D6711yescharacteristic
740C2#585×D6711yescharacteristic
subgroupG/H
centerC2×C4C24×D67
commutator, socle, cosocleC22×C67C26
FrattiniC22C25×D67
FittingQ8×#41×C67C2
prime radicalC2×#41×D67C22
hypercenterQ8×#41D67
hypocenterC67C2×Q8×#41
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ Q8×#41

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. Q8×#11761629C2semidirect
2. #22573791C2semidirect
3. Q8×#11761628C2semidirect
4. #41×Dic134C2semidirect
5. #22573788C2semidirect
6. #22573787C2semidirect
7. Q8×#11761627C2semidirect
8. Q82×D67C2semidirect
9. #557×D67C2semidirect
10. #554×D67C2semidirect
11. D4×Q8×D67C2semidirect
12. #533×D67C2semidirect
14. C2×C4×Q8×D67C2semidirect
15. Q8×#41×C67C2semidirect
18. Q8×Dic134C22semidirect
19. Q8×Dic134C22semidirect
20. #16864126C22semidirect
21. #16864125C22semidirect
22. #16864124C22semidirect
23. #16864123C22semidirect
24. #16864122C22semidirect
25. #16864121C22semidirect
26. #16864107C22semidirect
27. #16864106C22semidirect
28. #16864105C22semidirect
29. #16864104C22semidirect
30. #16864103C22semidirect
31. #16864102C22semidirect
32. #16864101C22semidirect
33. #16864100C22semidirect
34. Q8×D268C22semidirect
35. D4×Dic134C22semidirect
36. #16864061C22semidirect
37. Q8×C22⋊D67C22semidirect
38. #16864059C22semidirect
39. #16863953C22semidirect
40. #16863952C22semidirect
41. #16863951C22semidirect
42. #16863951C22semidirect
43. #16863950C22semidirect
44. #16863950C22semidirect
45. #16863949C22semidirect
46. #16863948C22semidirect
47. #16863948C22semidirect
60. C2×Q8×Dic67C22semidirect
61. C2×C4×Dic134C22semidirect
62. C2×#14524008C22semidirect
70. C4×Q8×D67C22semidirect
71. C4×Q8×D67C22semidirect
72. C4×Q8×D67C22semidirect
73. C4×Q8×D67C22semidirect
79. Q82×C67C22semidirect
80. #557×C67C22semidirect
81. #554×C67C22semidirect
82. D4×Q8×C67C22semidirect
83. #533×C67C22semidirect
85. C2×C4×Q8×C67C22semidirect
89. #41×D67Q8direct (N × H)
208. #11761629C2×Q8semidirect
209. #11761628C2×Q8semidirect
210. #11761627C2×Q8semidirect
221. Q8×D67C2×Q8semidirect
222. Q8×D67#41direct (N × H)
225. D4×D67C2×Q8semidirect
231. C2×C4×D67C2×Q8semidirect
272. #41×C67C2×Q8semidirect
301. Q8×C67C22×Q8semidirect
302. Q8×C67C2×#41semidirect
303. D4×C67C22×Q8semidirect
306. C2×C4×C67C22×Q8semidirect
313. C22⋊D67C22×Q8semidirect
316. C2×Dic67C22×Q8semidirect
323. D268C22×Q8semidirect
333. C4×D67C22×Q8semidirect
334. C4×D67C22×Q8semidirect
339. Dic134C22×Q8semidirect
340. Dic134C2×#41semidirect
370. D67Q8×#41direct (N × H)
378. Q8×#41D67direct (N × H)
386. C67C2×Q8×#41semidirect
392. Q82C2×D67semidirect
398. #557C2×D67semidirect
407. #554C2×D67semidirect
413. D4×Q8C2×D67semidirect
423. #533C2×D67semidirect
451. C2×C4×Q8C2×D67semidirect
582. #41Q8×D67direct (N × H)
677. Q8C2×Q8×D67semidirect
678. Q8#41×D67direct (N × H)
681. D4C2×Q8×D67semidirect
705. C2×C4C2×Q8×D67semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
Q8×#117616292
#225737912
Q8×#117616282
#41×Dic1342
#225737882
#225737872
Q8×#117616272
Q82×D672
#557×D672
#554×D672
D4×Q8×D672
#533×D672
C4×#41×D672
C2×C4×Q8×D672
Q8×#41×C672
C2×Q8×#4167